DIGITAL VERSION OF THE MATHERON REPRESENTATION THEOREM FOR INCREASING tau -MAPPINGS IN TERMS OF A BASIS FOR THE KERNEL.
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G. Matheron (1975) has given a fundamental representation theorem for increasing tau -mappings. He shows that for Euclidean constant images (subsets of the plane) every increasing tau -mapping admits a representation in terms of a union of erosions over the kernel of the mapping. The proof of the theorem goes through without essential alteration for discrete constant images (subsets of the grid Z multiplied by Z). Through the introduction of a basis for the kernel, a practical finite representation result can be achieved for digital images with some restriction on the class over which the representation holds.